The mathematics developed in this century will be the basis for the technological and scientiﬁc innovations developed in the next one. The thought processes, the ways of looking at things, the habits of mind used by mathematicians, computer scientists, and scientists will be mirrored in systems that will inﬂuence almost every aspect of our daily lives. If we really want to empower our students for life after school, we need to prepare them to be able to use, understand, control, and modify a class of technology that doesn’t yet exist. That means we have to help them develop genuinely mathematical ways of thinking. In this paper, we’ve tried to describe some of these mental habits. Our curriculum development efforts will attempt to provide students with the kinds of experiences that will help develop these habits and put them into practice.